Why ELO ratings affect the winning rate

All players make more mistakes in complex positions than in simple
ones.

Most players are capable of finding the obvious answer to a violent
threat, and therefore make fewer mistakes in normal attack and
defense than they do in positions where the objectives are more
vague. [1]

The weaker player in a game should choose an opening that produces a
violent confrontation right out of the book moves, and try to play a
short game.

The stronger player should choose an opening that leads to a complex
game, but in which the real fighting is delayed as long as possible;
and is best served by playing a long and complex game. These goals
are more important than trying for an opening advantage against the
weaker player.

[1] The inner meaning of "a waiting move" is
"give him enough rope to hang himself".

The above chain of reasoning is original, and you have not seen it
elsewhere. Go back and read it again. By reading it, you probably
added 50 points to your rating.

If you have a tendency to do well against strong players and poorly
against weaker players, reading this could add 150 points to your
rating. Go back and read it again, think about it, and make it a
part of your play.

And In Closing, May I Say

Advantage affects the winning rate because the players make errors,
but the player who has the advantage is less harmed by his errors.

ELO ratings affect winning rates because the players make errors,
but the stronger player makes fewer and smaller ones.